Complete the following sequence:

-35, -44, -39, -34, -19, 0, 29, ?, ?

(In reply to

re: Puzzle Solution by Jack)

The foregoing observation leads one to surmise that my earlier post may not be fully lucid in terms of clarity.

Accordingly, I will now try to explain the various steps inclusive

of my earlier post to the best of my ability.

It may be recalled that the first few prime numbers are as follows:

1st prime number = 2,

2nd prime number =3,

3rd prime number = 5,

4th prime number = 7,

5th prime number = 11,

6th prime number= 13,

7th prime number = 17,

8th prime number = 19,

9th prime number = 23,

10th prime number = 29,

11th prime number = 31,

12th prime number = 37,

13th prime number = 41, and so on.......

Reference : http://en.wikipedia.org/wiki/Prime_number

Since, U(x) = (3+x)th prime number as defined in terms of last post, we must have:

U(1) = 4th prime number =7,

U(2) = 5th prime number =11,

U(3) = 6th prime number = 13, and in a similar manner:

U(4) = 17, U(5)= 19, U(6)= 23, U(7)= 29, U(8)= 31, U(9)= 37, and so on....

T(x) = x-6, and therefore:

T(1) = -5, T(2) = -4, T(3) = -3, T(4) = -2, T(5) = -1, T(6) = 0

T(7) = 1, T(8) = 2, T(9) = -5, and so on.....

S(x) = T(x)*U(x), where S(x) is the xth term of the given sequence

Accordingly, we must have:

S(1) = T(1)*U(1) = -5*7 = 35

S(2) = -4*11 = -44

S(3) = -3*13 = -39

S(4) = -2*17 = -34

S(5) = -1*19 = -19

S(6) = 0*23 = 0

S(7) = 1*29 = 29

S(8) = 2*31= 62

S(9) = 3*37 = 111

Consequently, the required misssing terms are 62 and 111.

Please feel free to comment in case you have further queries regarding this methodology.

*Edited on ***April 18, 2008, 1:31 pm**